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<div class="titlepage"><div><div><h6 class="title">
<a name="sort.single_thread.spreadsort.sort_hpp.rationale.hybrid_radix"></a><a class="link" href="hybrid_radix.html" title="Hybrid Radix">Hybrid
            Radix</a>
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<p>
              There a two primary types of radix-based sorting:
            </p>
<p>
              Most-significant-digit Radix sorting (MSD) divides the data recursively
              based upon the top-most unsorted bits. This approach is efficient for
              even distributions that divide nicely, and can be done in-place (limited
              additional memory used). There is substantial constant overhead for
              each iteration to deal with the splitting structure. The algorithms
              provided here use MSD Radix Sort for their radix-sorting portion. The
              main disadvantage of MSD Radix sorting is that when the data is cut
              up into small pieces, the overhead for additional recursive calls starts
              to dominate runtime, and this makes worst-case behavior substantially
              worse than <span class="emphasis"><em>𝑶(N*log(N))</em></span>.
            </p>
<p>
              By contrast, <code class="literal"><code class="computeroutput"><a class="link" href="../../../../../boost/sort/spreadsort/integer__idm46498512795392.html" title="Function template integer_sort">integer_sort</a></code></code>,
              <code class="literal"><code class="computeroutput"><a class="link" href="../../../../../boost/sort/spreadsort/float_so_idm46498513989248.html" title="Function template float_sort">float_sort</a></code></code>,
              and <code class="literal"><code class="computeroutput"><a class="link" href="../../../../../boost/sort/spreadsort/string_s_idm46498512563328.html" title="Function template string_sort">string_sort</a></code></code>
              all check to see whether Radix-based or Comparison-based sorting have
              better worst-case runtime, and make the appropriate recursive call.
              Because Comparison-based sorting algorithms are efficient on small
              pieces, the tendency of MSD <a href="http://en.wikipedia.org/wiki/Radix_sort" target="_top">radix
              sort</a> to cut the problem up small is turned into an advantage
              by these hybrid sorts. It is hard to conceive of a common usage case
              where pure MSD <a href="http://en.wikipedia.org/wiki/Radix_sort" target="_top">radix
              sort</a> would have any significant advantage over hybrid algorithms.
            </p>
<p>
              Least-significant-digit <a href="http://en.wikipedia.org/wiki/Radix_sort" target="_top">radix
              sort</a> (LSD) sorts based upon the least-significant bits first.
              This requires a complete copy of the data being sorted, using substantial
              additional memory. The main advantage of LSD Radix Sort is that aside
              from some constant overhead and the memory allocation, it uses a fixed
              amount of time per element to sort, regardless of distribution or size
              of the list. This amount of time is proportional to the length of the
              radix. The other advantage of LSD Radix Sort is that it is a stable
              sorting algorithm, so elements with the same key will retain their
              original order.
            </p>
<p>
              One disadvantage is that LSD Radix Sort uses the same amount of time
              to sort "easy" sorting problems as "hard" sorting
              problems, and this time spent may end up being greater than an efficient
              <span class="emphasis"><em>𝑶(N*log(N))</em></span> algorithm such as <a href="http://en.wikipedia.org/wiki/Introsort" target="_top">introsort</a>
              spends sorting "hard" problems on large data sets, depending
              on the length of the datatype, and relative speed of comparisons, memory
              allocation, and random accesses.
            </p>
<p>
              The other main disadvantage of LSD Radix Sort is its memory overhead.
              It's only faster for large data sets, but large data sets use significant
              memory, which LSD Radix Sort needs to duplicate. LSD Radix Sort doesn't
              make sense for items of variable length, such as strings; it could
              be implemented by starting at the end of the longest element, but would
              be extremely inefficient.
            </p>
<p>
              All that said, there are places where LSD Radix Sort is the appropriate
              and fastest solution, so it would be appropriate to create a templated
              LSD Radix Sort similar to <code class="literal"><code class="computeroutput"><a class="link" href="../../../../../boost/sort/spreadsort/integer__idm46498512795392.html" title="Function template integer_sort">integer_sort</a></code></code>
              and <code class="literal"><code class="computeroutput"><a class="link" href="../../../../../boost/sort/spreadsort/float_so_idm46498513989248.html" title="Function template float_sort">float_sort</a></code></code>.
              This would be most appropriate in cases where comparisons are extremely
              slow.
            </p>
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      Ross, Francisco Tapia, Orson Peters<p>
        Distributed under the <a href="http://boost.org/LICENSE_1_0.txt" target="_top">Boost
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